"Economics is not a science," said the other day a friend of mine, a well known expert in computers and information systems. The image he has in mind is probably these that give these "economists" that one hears or sees in the French media, real sophists which are able to demonstrate everything and its opposite, and change their mind with always the same confidence. But this image is superficial.

"If you read Adam Smith, I answered, or Alfred Marshall, or Léon Walras, or John Hicks, or closer to us Ivar Ekeland and some others, you would see that

*there is*an economic science. However I must confess that it took me time to understand that... "

Indeed the economics classes that I suffered at ENSAE in 1963-65 were so dogmatic that they could only convince students endowed with a docile memory - while my own memory, as restive as a skittish horse, agrees to hold only what I fully understand. Ekeland opened for me the door of economics with an article in

*La Recherche*in 1976, while I stumbled on the limits of the interpretation of statistics.

When in 1983 I set up a mission of economic studies at CNET, engineers and researchers with whom I worked had the same prejudices that my friend. "Economics, they said, is a soft science". They believed that the economist is a dishonest lawyer whom the leaders instruct to "demonstrate" the profitability of projects they have already chosen.

* *

These engineers and researchers adhered without doubt, like my friend, to the hierarchy of science that Comte proposed with mathematics at the top. Mathematics give us the best example of rigorous reasoning and perfect demonstration,

**but**their arguments and proofs are based on axioms which, having been chosen initially, are not demonstrated nor demonstrable: for sure the mathematician reasons rigorously, but his starting point is

*hypothetical*.

In order to be clear, consider the geometry of the triangle: the sum of the angles is 180°, the surface is calculated using a well known formula and we also know the rules which allow to say if two triangles are equal or similar. But these results are accurate only if the triangles are in a space of zero curvature or, as they say, a "Euclidean" space.

If the triangles are plotted on a sphere, many of these results are false: seamen, as well as aviators, must take that into account. Moreover Einstein showed that at the scale of the Cosmos the space is curved. The Euclidean space is rich in properties that make it convenient for reasoning and it provides at short distances a good approximation of the real space, but this is only an approximation.

Thus the art of the mathematician is not, as those who follow Comte believe, to state absolute truths but to choose a bunch of non contradictory axioms and to deploy rigorously their consequences. The truth of mathematics is

*apodictic*: it lays in rigorous deductions which are suspended to assumptions.

Mathematics explore the world of thought under the only constraint of non-contradiction: since antiquity, they are a branch of logic which is itself a branch of philosophy - and it does not matter, considering the weight of this historical and logical fact, if our times attaches to philosophy a superficial "literary" image.

* *

Economics applies the same approach to a restricted domain, that of the material well-being of the population which depends on the distribution of natural resources, production and exchange – and, in more detail, of income distribution, investment, innovation, public services, taxation, externalities, regulation of markets and so on.

The art of the economist consists to make in a first step assumptions about natural resources, the production function, the utility function etc., and then to deduce by reasoning the form of the economic regime of one population and the level of its well-being.

He will then change these assumptions in order to consider a diversity of situations and explore, with his imagination, a diversity of economic systems. Between these regimes, he will advocate that which is Pareto optimal, i. e. which allows to obtain the maximum well-being given the distribution of available resources : one can say that economics is primarily a

*theory of efficiency*.

Every

*economic model*relies, as a mathematical theory, on a bunch of assumptions. Thus the filiation with mathematics is at the root of economics, and this fact goes much deeper that the applications of differential calculus or tensor calculus that abound in the literature - some of them serious and justified, some intended to give to the book or article an appearance of scientificity.

* *

The function of a model is to provide, by

*simulation*, a representation of a world where we assume that the hypotheses are true. Sometimes this simulation will be purely mental: this world appears before the imagination of the economist as in an exercise of science fiction (which is what happened to me when I modeled the "new economy").

But a computation is often necessary: reasoning cannot be conclusive when a decision has two effects of opposite sign. A firm increases the price of his product: it increases the revenue by unit sold but lowers the demand, and the evolution of the turnover depends on the balance between these two effects. It is the same if a State increases a tax rate etc.

In such cases the economist goes beyond pure reasoning and considers

*facts*, like the mathematician, using the geometry of the triangle, place markers on the ground he intends to measure. But before applying a model he must verify that its schematic provides an acceptable approximation: the mathematician knows that Euclidean geometry provides an acceptable approximation of the surface of Earth up to a distance of some kilometers.

Just as the demarcation of land makes it possible to calculate a surface, statistics provides data for the calibration of equations : economics which, in terms of reasoning, is akin to mathematics, is also similar to experimental science in its relation to reality. No doubt it can not perform these controlled experiments that are done in laboratories, but the most significative part of the experimental method lies in the subjection of the reasoning under the yoke of factual findings, the confrontation with the truth of facts.

Science, one might say, has two sides: 1) the art of reasoning on assumptions, leaving aside the question of realism, 2) the approach that confronts these assumptions to the situation considered. Thus it appears that economics meets the criteria of scientificity: considering the Popperian "falsifiability", a theory is not scientific 1) if it is based on assumptions that contradict each other, 2) if it includes logically false deductions, 3) if, in his degree of approximation, its assumptions are contradicted by the facts.

Sometimes the calculation is difficult and requires to use a computer that will compute automatically: this will bring to economics a powerful tool to explore simulations, but this aid is accompanied by some danger.

Econometricians, eager to let their models run, do not always care enough on the approximations that statistics or national accounts include. Worse still, its reasoning hardly masters the simultaneous interplay of hundreds or thousands of equations in the econometric model and a lazy economist will often be a dupe of the results that the automaton provides.

* *

Back to the hierarchy of sciences. If we give priority to the rigor of reasoning, to the formal quality of the methods, then we will place mathematics at the top as did Comte and as still does today the French educational system.

But we can also, and perhaps we should, give priority to

*action*and to the practical constraints which life confronts everybody, every institution, every nation, and eventually mankind. Indeed nobody escapes these requirements nor the responsibility they entail!

The ranking of sciences will be quite different if one adopts this latter point of view. The realm of action is that of urgency and uncertainty: the mathematics know neither one nor the other. Their position, certainly honorable, appears similar to that occupied by the gym next to physical activity: a useful preparation, a necessary exercise, but which can not fill alone a human life.

By cons disciplines that inform action are now placed at the top: economics, history, strategy. Some of them lack the same rigor as mathematics, their development does not have the same formal richness, but they talk about what we do, they inform our decisions as well as our choices. What science could be better?

* *

The economist who is trained to explore by simulation the various possible economic worlds, and who exercised his mind to deduce the consequences of a bunch of assumptions, knows, when faced with a real and concrete economy, represent it schematically and diagnose more quickly and surely than others what his economic regime is, what level of welfare its population can achieve and what needs to be done for efficiency; he also knows how to discern the future consequences of decisions make today by politicians, entrepreneurs and speculators.

Its conclusions may not have the same degree of certainty that the proof of a theorem, but who cares! It is the same for generals on the battlefield, and some generals master better than others the art of seeing clearly and act justly in uncertainty: the economist must also strive to master the art of correct reasoning, of responsible action in uncertain circumstances.

To the man of action, mathematical training provides a taste for exact reasoning and rigorous logic: it is a weapon against the seductions of sophistry. But mathematics ignore the constraints of emergency as well as the fog in which we have to take the most important decisions in our lives (where is certainty when we choose a profession, when we build a couple?). So we need to learn other disciplines, other approaches if we want science to be, as it should be, a preparation and a weapon for action.

* *

Among the criticisms that some people make to economics, some target its purpose: economics does not speak, they say, of happiness and equity.

These allegations are both founded and abusive. They are founded, because it is true that the material well-being is not happiness, that the pursuit of efficiency is indifferent to equity. But why do they ask to economics for more than it can bring? We accept that a plumber is not at the same time a dentist; why would we require economics to support, in addition to efficiency that is its own purpose, happiness and equity?

These criticisms target in fact the

*economism*, which claims that economics is able to answer all the problems of society - while it is obviously no more capable of that than are the other specialties.

For the accuracy of judgment as for the correctness of action it is important to have clean, sharp tools. That is why I believe that attempts, like those of Amartya Sen, to import in the economy the requirements of equity and happiness, are misguided and provide a paradoxical support to the claims of economism.

Concerning equity, it is better to study and apply the

*Theory of Justice*by John Rawls, which should be fundamental for jurists and legislators. Concerning happiness those who, once past adolescence, say they want to achieve it without material well-being are either saints or hypocrites and the second hypothesis is likely. Yes, the source of happiness lies in the balance that intimate wisdom provides: but a wise man, even if he is sober, do not despise earthly food nor the pleasures of life.

* *

I concede to my friend that we encounter, among the economists, some pranksters whose peremptory speeches, whose papers saturated with equations, let us think about how prostitutes stir their bottom in order to attract clients. Their proportion is probably not higher than in other professions, but they are perhaps more noticeable.

Great economists are excellent mathematicians, but they have no desire to impress and their papers are sober in equations. They are not easy to read - economics is a difficult discipline - but the effort of the reader is amply rewarded. When he encounters one of them, he feels for him recognition and even, dare I say, affection : "we expected to see an author, and we found a man" (Blaise Pascal ,

*Pensées*, XXVIII).

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